Crossover scales at the critical points of fluids with electrostatic interactions

Critical charge and density coupling in ionic spherical models

We investigate ionic criticality on the basis of a specially devised spherical model that accounts both for Coulomb and nonionic forces in binary systems. We show in detail here the consequences of the entanglement of density and charge correlation functions G_{NN} and G_{ZZ} on criticality and screening. We also show on this soluble model how, because of electroneutrality, the long-range Coulomb interactions do not change the universality class of criticality in the model driven primarily by sufficiently attractive nonionic interactions. Near criticality, G_{NN} and G_{ZZ} are fully decoupled in charge symmetric systems. However, in more realistic nonsymmetric models, charge and density fluctuations couple in leading order so that the charge and density correlation lengths diverge asymptotically in a similar way. Similarly, the Stillinger-Lovett sum rule, which characterizes a conducting fluid, is violated at criticality in nonsymmetric models when the critical-point density-decay exponent η vanishes. In addition, if quantum effects are accounted for semiclassically by incorporating algebraically decaying interactions, G_{ZZ} decays only as a power law in the whole phase space, contrary to the usually expected exponential Debye screening. We expect these results on this soluble toy model to be general and to reveal general mechanisms ruling ionic criticality.

Ginzburg criterion for ionic fluids: the effect of Coulomb interactions

The effect of the Coulomb interactions on the crossover between mean-field and Ising critical behavior in ionic fluids is studied using the Ginzburg criterion. We consider the charge-asymmetric primitive model supplemented by short-range attractive interactions in the vicinity of the gas-liquid critical point. The model without Coulomb interactions exhibiting typical Ising critical behavior is used to calibrate the Ginzburg temperature of the systems comprising electrostatic interactions. Using the collective variables method, we derive a microscopic-based effective Hamiltonian for the full model. We obtain explicit expressions for all the relevant Hamiltonian coefficients within the framework of the same approximation, i.e., the one-loop approximation. Then we consistently calculate the reduced Ginzburg temperature t(G) for both the purely Coulombic model (a restricted primitive model) and the purely nonionic model (a hard-sphere square-well model) as well as for the model parameters ranging between these two limiting cases. Contrary to the previous theoretical estimates, we obtain the reduced Ginzburg temperature for the purely Coulombic model to be about 20 times smaller than for the nonionic model. For the full model including both short-range and long-range interactions, we show that t(G) approaches the value found for the purely Coulombic model when the strength of the Coulomb interactions becomes sufficiently large. Our results suggest a key role of Coulomb interactions in the crossover behavior observed experimentally in ionic fluids as well as confirm the Ising-like criticality in the Coulomb-dominated ionic systems.

Critical behavior on approaching a special critical point in a complex fluid

The critical behavior of osmotic susceptibility is investigated in the re-entrant complex mixture 1-propanol (P)+water (W)+potassium chloride (KCl) through light-scattering measurements. The measurements are performed on approaching a special critical point [i.e., the double critical point (DCP)] in this mixture, along the line of upper critical solution temperatures (T(U)'s), by varying t from the high temperature one-phase region. The light-scattering data analysis emphasizes the need for corrections to the asymptotic Ising behavior and yields very large magnitudes for the correction-to-scaling amplitudes A(1) and A(2), with the first-correction amplitude A(1) being negative, signifying a nonmonotonic crossover behavior of the susceptibility exponent in this mixture. For the T(U) closest to the DCP, the effective susceptibility exponent gamma(eff) displays a nonmonotonic crossover from its nearly doubled three dimensional (3D)-Ising value toward its nearly double mean-field value with an increase in t. While for that far away from the DCP, it displays a nonmonotonic crossover from its single-limit Ising value toward a value slightly lower than its mean-field value of 1 with an increase in t. This feature of the effective susceptibility exponent is interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from lower values in the nonasymptotic high t region. The renormalized Ising regime extends over a larger t range for the sample (or T(U)) closest to the DCP when compared to that far away from it. The in-between T(U)'s display a trend toward shrinkage in the renormalized Ising regime as T(U) shifts away from the DCP. Nevertheless, the crossover to the mean-field behavior is completed only beyond t>10(-2) for the T(U)'s studied. The observed crossover behavior is attributed to the presence of strong ion-induced clustering in this mixture, as revealed by various structure probing techniques, while the observed unique trend in the crossover behavior is discussed in terms of the varying influence of the DCP on the critical behavior along the T(U) line. The crossover behavior for the T(U)'s is pronounced and more sharp compared to the T(L)'s (lower critical solution temperatures) [U. K. Pradeep, J. Chem. Phys. 129, 134506 (2008)] in this mixture, although there exists no difference in the growth of the mesoscale clusters in the lower and upper one-phase regions in this mixture. Our observations suggest the need to look at the crossover behavior probably from two perspectives, namely, the dielectric effect and the clustering effect. The effective susceptibility exponent as a function of the field variable t(UL), instead of the conventional variable t, displays a sharp nonmonotonic crossover from its asymptotic 3D-Ising value ( approximately 1.24) toward a value slightly lower than its nonasymptotic mean-field value of 1, as that observed in the t analysis for the T(U) far away from the influence of the DCP.

Ion-induced multiply reentrant liquid-liquid transitions and the nature of criticality in ethanol-water mixture

We report a quite unusual feature of four liquid-liquid reentrant transitions in ethanol (E)+water (W)+ammonium sulfate mixture by meticulous tuning of the ammonium sulfate concentration in a narrow range, as a function of temperature, at atmospheric pressure. Detailed exploration of the intricate phase behavior in terms of E/W sections shows that the range of triple reentrance shrinks with increasing E/W. The behavior of osmotic susceptibility is investigated by light scattering, near the critical point, in the one-phase region by varying the temperature at fixed concentration of the components, in a particular E/W section. The critical exponent of susceptibility (gamma) and correlation length (nu) are observed to have Fisher renormalized Ising values [Phys. Rev. 176, 237 (1968)], with gamma(r)=1.41 and nu(r)=0.718. The effective susceptibility exponent, gamma(eff), exhibits a sharp, nonmonotonic crossover from Ising to mean-field critical behavior, which is completed outside the critical regime. The amplitude of the correlation length, xi(o)(=21.2+/-0.4 A), deduced from light scattering experiment, is an order of magnitude larger than the typical values in usual aqueous electrolyte systems. This value of xi(o) is further verified from small-angle x-ray scattering (SAXS) experiments and found to be consistent. SAXS experiments on the critical sample reveal the presence of long-ranged intermolecular correlations, leading to supramolecular structuring, at a temperature far away from the critical point. These results convincingly demonstrate that the finite length scale arising due to the structuring competes with the diverging correlation length of critical concentration fluctuations, which influences the nonasymptotic critical behavior in this aqueous electrolyte system. The sulphate ions play a dominant role in both structuring and the complex phase behavior.

Criticality in aqueous solutions of 3-methylpyridine and sodium bromide

We address a controversial issue regarding the nature of critical behavior in ternary electrolyte solutions of water, 3-methylpyridine, and sodium bromide. Earlier light-scattering studies showed an anomalous critical behavior in this system that was attributed to the formation of a microheterogeneous phase associated with ion-molecule clustering [M.A. Anisimov, J. Jacob, A. Kumar, V.A. Agayan, and J. V. Sengers, Phys. Rev. Lett. 85, 2336 (2000)]], while some other investigators subsequently found this system to exhibit ordinary Ising-like critical behavior. This contradiction forced us to revisit the problem and perform an accurate and comprehensive study of light scattering in this system paying attention to the achievement of thermodynamic equilibrium, hysteresis effects, aging, and prehistory of the samples, and a possible role of impurities. We show that properly aged, equilibrium samples of aqueous solutions of 3-methylpyridine with NaBr exhibit universal Ising-like critical behavior, typical for other aqueous solutions. No evidence for an equilibrium microheterogeneous phase was found. We have been able to reproduce anomalous behavior (similar to that reported initially) in a fast run on a freshly prepared sample. We attribute the observed anomalies to mesoscopic nonequilibrium aggregates, possibly associated with supramolecular restructuring in aqueous solutions. To support this conclusion we performed a study of aqueous solutions of 3-methylpyridine without NaBr and have found long-living nonequilibrium states in aqueous solutions of 3-methylpyridine.

Ionic criticality: an exactly soluble model

Gas-liquid criticality in ionic fluids is studied in exactly soluble spherical models that use interlaced sublattices to represent hard-core multicomponent systems. Short-range attractions in the uncharged fluid drive criticality, but charged ions do not alter the universality class. Debye screening remains exponential at criticality in fully ion-symmetric 1:1 models. However, ionic asymmetry couples charge and density fluctuations in a direct manner: The charge correlation length then diverges precisely as the density correlation length and the Stillinger-Lovett rule is violated at criticality.

Universality class of criticality in the restricted primitive model electrolyte

The 1:1 equisized hard-sphere electrolyte or restricted primitive model has been simulated via grand-canonical fine-discretization Monte Carlo. Newly devised unbiased finite-size extrapolation methods using loci in the temperature-density or (T,rho) plane of isothermal rho(2-k) vs pressure inflections, of Q identical with<m(2)>(2)/<m(4)> maxima, and of canonical and C(V) criticality, yield estimates of (T(c),rho(c)) to +/-(0.04,3)%. Extrapolated exponents and Q ratio are (gamma,nu,Q(c)) = [1.24(3), 0.63(3); 0.624(2)], which support Ising (n = 1) behavior with (1.23(9), 0.630(3); 0.623(6)), but exclude classical, XY (n = 2), self-avoiding walk (n = 0), and n = 1 criticality with potentials varphi(r)>Phi/r(4.9) when r-->infinity.

Precise simulation of criticality in asymmetric fluids

Extensive grand canonical Monte Carlo simulations have been performed for the hard-core square-well fluid with interaction range b=1.5 sigma. The critical exponent for the correlation length has been estimated in an unbiased fashion as nu=0.63+/-0.03 via finite-size extrapolations of the extrema of properties measured along specially constructed, asymptotically critical loci that represent pseudosymmetry axes. The subsequent location of the critical point achieves a precision of five parts in 10(4) for Tc and about 0.3% for the critical density rhoc. The effective exponents gamma+(eff) and beta(eff) indicate Ising-type critical-point values to within 2% and 5.6%, respectively, convincingly distinguishing the universality class from the "nearby" XY and n=0 (self-avoiding walk) classes. Simulations of the heat capacity CV(T,rho) and d2psigma/dT2, where psigma is the vapor pressure below Tc, suggest a negative but small Yang-Yang anomaly, i.e., a specific-heat-like divergence in the corresponding chemical potential derivative (d2 musigma/dT2) that requires a revision of the standard asymptotic scaling description of asymmetric fluids.

Criticality and crossover in accessible regimes

The near-critical behavior of (d = 3)-dimensional Ising-model ferromagnets or simple lattice gases with equivalent first, second, and third nearest-neighbor interactions is studied through Monte Carlo simulations using histogram reweighting techniques and comparisons with series expansions. By carefully analyzing numerical data from relatively small finite systems using scaling and extrapolation methods, it is demonstrated that one can reliably estimate critical exponents, critical temperatures, and universal amplitude ratios, thereby distinguishing convincingly between different "nearby" universality classes and revealing systematic crossover effects. This study is preparatory to extending similar techniques to study criticality in continuum fluid models lacking symmetries, with Coulomb interactions, etc.

Identity of the universal repulsive-core singularity with Yang-Lee edge criticality

Lattice and continuum fluid models with repulsive-core interactions typically display a dominant, critical-type singularity on the real, negative activity axis. Lai and Fisher recently suggested, mainly on numerical grounds, that this repulsive-core singularity is universal and in the same class as the Yang-Lee edge singularities, which arise above criticality at complex activities with positive real part. A general analytic demonstration of this identification is presented here using a field-theory approach with separate representations of the repulsive and attractive parts of the pair interactions.